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<p class="menu"><a>1206</a>:<a>Test 4</a> <a class="aleft">Logout</a></p>
<div class="problem">
<div class="divproblemstatementheading"> <h3>Test 4, Problem 3</h3>
</div>
<div class="divproblemstatement">
A lamina of density 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">
  <mi>&#x03B4;<!-- δ --></mi>
  <mo>=</mo>
  <mn>.75</mn>
  <mtext>&#xA0;</mtext>
  <mfrac>
    <mtext>kg</mtext>
    <msup>
      <mtext>m</mtext>
      <mn>2</mn>
    </msup>
  </mfrac>
</math> is bounded by the graphs of functions:
<p class="mathformula">
<math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mfrac>
    <msup>
      <mi>x</mi>
      <mn>2</mn>
    </msup>
    <mn>4</mn>
  </mfrac>
</math>
 and 
 <math xmlns="http://www.w3.org/1998/Math/MathML">
  <mi>g</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mfrac>
    <mi>x</mi>
    <mn>2</mn>
  </mfrac>
</math>
(see the picture below)</p>
<object type="image/svg+xml" name="omap" data="pics/problem1.svg" height="300px"><table align="center" border="2"><tr><td align="center">You should see a maps within an &lt;object&gt;-tag here<br><br><b>YOUR BROWSER DOESN'T SUPPORT EMBEDED HTML-OBJECTS.<br><br>Please update!</b></td></tr></table></object></div>
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<div class="questions">
<div class="diveditorheading"><h3>Question 1</h3>
</div>
<div class="diveditor">
Set up an integral formula to compute the moment of the lamina around x-axis:
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" class="editablemath answerform">
	<mrow>
		<msub>
			<mi>M</mi>
			<mi>x</mi>
		</msub>
		<mo>=</mo>
		<msubsup>
			<mo>&#x222B;<!-- ∫ --></mo>
			<mrow class="selectable empty"><mphantom>X</mphantom></mrow>
			<mrow class="selectable empty"><mphantom>X</mphantom></mrow>
		</msubsup>
		<mrow class="selectable empty">
			<mphantom>X</mphantom>
		</mrow>
		<mspace width="thinmathspace" />
		<mi>d</mi>
		<mrow class = "selectable empty">
			<mphantom>X</mphantom>
		</mrow>
	</mrow>
</math>
</div>

<div class="diveditorheading"><h3>Question 2</h3></div>
<div class="diveditor">
Set up an integral formula to compute the moment of the lamina around y-axis:
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" class="editablemath answerform">
	<mrow>
		<msub>
			<mi>M</mi>
			<mi>y</mi>
		</msub>
		<mo>=</mo>
		<msubsup>
			<mo>&#x222B;<!-- ∫ --></mo>
			<mrow class="selectable empty"><mphantom>X</mphantom></mrow>
			<mrow class="selectable empty"><mphantom>X</mphantom></mrow>
		</msubsup>
		<mrow class="selectable empty">
			<mphantom>X</mphantom>
		</mrow>
		<mspace width="thinmathspace" />
		<mi>d</mi>
		<mrow class = "selectable empty">
			<mphantom>X</mphantom>
		</mrow>
	</mrow>
</math>
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<div id="help">
<h3>User's Manual</h3>
<p>
Key combinations that work:
<ul>
<li>Left-click on the parts of the equation to start typing</li>
<li><span class="boxed">A</span> - <span class="boxed">Z</span> letters and digits work as they usually do</li>
<li>Arithmetic operations <span class="boxed">+</span>, <span class="boxed">-</span>, <span class="boxed">*</span> (<span class="boxed">Shift</span> + <span class="boxed">8</span>), <span class="boxed">/</span> and <span class="boxed">^</span> (<span class="boxed">Shift</span> + <span class="boxed">6</span>) are recognized</li>
<li><span class="boxed">Space</span> creates white spaces. Use it to break numbers and symbol sequences apart.</li>
<li><span class="boxed">(</span>, <span class="boxed">[</span>, <span class="boxed">{</span>, <span class="boxed">|</span> buttons create matched delimiters </li>
<li>Backspace erases an item to the left of the cursor, if there is anything in the container template.</li>
<li>Left and right arrow keys navigate around the equation</li>
</ul>
The output looks nicer if you have STIX fonts installed (available for free from <a href="http://www.stixfonts.org/">STIX fonts web-site</a>).<br />
Equation editor tries to format the equation so that it is visually unambiguous. It wraps parts of the equation in grayed out parenthesis or adds grayed out cross to indicate multiplication if the rendering results might be interpreted ambiguously.
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